How do I control the armature in weight paint mode?
The armature has to be in Pose mode, then Shift-select the mesh and go into Weight Paint mode.

If you have selection set to Right-click in Preferences then:


Sample weight (color) with Ctrl LMB
Select bone with RMB


If you have selection set to Left-click in Preferences:


Sample weight (color) with Ctrl RMB
Select bone with  Ctrl LMB


Independently of Select with option:


Paint with LMB
Rotate, Move, Scale bone with R, G, S
Paint gradient with Alt LMB